Boolean with wireframe on mesh
If this is something like what you're after...




Select all edges, CtrlB bevel, by width, with a moderate even number of segments (here,6)
CtrlKeypad - reduce the selection back to the original latitudes and longitudes
O turn on proportional editing, Connected, Sphere fall-off, small radius
AltS scale along normals.
Select the smallest 'large' face, ShiftG select similar by area > 'Greater Than' to select all the large faces, and I inset them a little..





With  Autosmooth switched on, maybe have a play with the new Weighted
Normal modifier, by face area, to get the look you want without
subdivision.